WASHINGTON — Addressing concerns about rising premiums and dwindling competition, Health and Human Services Secretary Sylvia Burwell asserted Thursday that the federal health law’s insurance markets clearly are sustainable.

Willingness by Congress to help smooth out problems would definitely help, Burwell told reporters, but it is not absolutely essential. Congressional Republicans committed to repealing “Obamacare” are unlikely to assist.

HealthCare.gov and other state-level markets provide taxpayer subsidized private health insurance and now cover about 11 million people. “Even using the administrative tools that we have,” those markets remain viable, Burwell said.

Asked if they were sustainable even without legislative fixes, Burwell answered, “Yes.”

Burwell’s stance reflects resolve by the Obama administration to mount a successful 2017 sign-up season in the face of a new round of problems for the president’s signature domestic legislation.

Premiums in many areas are expected to go up by double digits and some insurers are bailing out or scaling back after having lost hundreds of millions of dollars. Going into their fourth year, the law’s health insurance markets don’t seem to be on a stable footing yet. But they are also unlikely to implode, because subsidies will cushion the impact of premium increases for most customers.

Earlier this week, Senate Majority Leader Mitch McConnell, R-Ky, said the health care overhaul “can’t possibly go on like it is.” He predicted it “will be revisited by the next president, whoever that is.” Long an opponent of the overhaul, McConnell favors its repeal.

Burwell said she hasn’t yet set a goal yet for 2017 enrollment but that she believes it will continue to grow. She cited steps the administration is taking to attract more customers, including:

—Direct outreach to people who paid a tax penalty this year for being uninsured. “Now people who have paid that penalty will be receiving communication at a point in time when they can do something about it,” she said.

—An improved tool for HealthCare.gov customers to compare different insurance plan options.

—A better system for resolving documentation problems with citizenship, legal residence and income. Unresolved paperwork issues have led to tens of thousands of customers being dropped from coverage or losing their subsidies.

—A focus on attracting healthy customers of any age, and not just the 18- to 34-year-olds, whose premiums help cross-subsidize older adults.